MATLAB: How to evaluate a double integral using the trapezoidal rule equation

double integration trapezoidal rule

Here's what I have so far
function [ I ] = myTrapz2D( f, x0, xn, y0, yn, nx, ny ) 
dx = (xn - x0)/nx;
dy = (yn - y0)/ny;
i = 1;
sumx = zeros(nx,1);
sumy =zeros(ny,1);
 while i < nx
    xi = x0 + i*dx;
    sumx(i) = f(xi);
    i = i+1;
end
sumx = sum(sumx);
Ix = ((dx)/2)*(f(x0)+f(xn)+(2*sumx));
fd = Ix(y);
 while i < ny
    yi = y0 + i*dy;
    sumy(i) = fd(yi);
    i = i+1;
end
sumy = sum(sumy);
 I =((dy)/2)*(fd(y0)+fd(yn)+(2*sumy));
  end
not sure if it's correct at all but it has to be solved using some variation of the equation for I that I used. I keep getting an error that there aren't enough input arguments. There are my input arguments: f = @(x,y) x.^2 – (2*y.^2) + (x.*y.^3); x0 = 0; xn = 2; y0 = -1; yn = 1; nx = 8; ny = 8;

Best Answer

You don't need to program the trapezoidal rule in two dimensions.
Just call the trapezoidal rule in one dimension twice. In the section "Multiple Numeical Integrations" under
https://de.mathworks.com/help/matlab/ref/trapz.html
is an example with the MATALB implementation of the trapezoidal rule "trapz".
Best wishes
Torsten.
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